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- 15:24, 21 October 2017 (diff | hist) . . (-26) . . Mozyrska-Torres logarithm at 1
- 15:22, 21 October 2017 (diff | hist) . . (+61) . . Mozyrska-Torres logarithm is positive on (1,infinity)
- 15:22, 21 October 2017 (diff | hist) . . (+1) . . Mozyraska-Torres logarithm is negative on (0,1)
- 15:22, 21 October 2017 (diff | hist) . . (+65) . . Mozyraska-Torres logarithm is negative on (0,1)
- 15:22, 21 October 2017 (diff | hist) . . (-1) . . Mozyraska-Torres logarithm is negative on (0,1)
- 15:21, 21 October 2017 (diff | hist) . . (0) . . m Mozyrska-Torres logarithm is positive on (1,infinity) (Tom moved page Mozyraska-Torres logarithm is positive on (1,infinity) to Mozyrska-Torres logarithm is positive on (1,infinity))
- 15:21, 21 October 2017 (diff | hist) . . (+67) . . N Mozyraska-Torres logarithm is positive on (1,infinity) (Tom moved page Mozyraska-Torres logarithm is positive on (1,infinity) to Mozyrska-Torres logarithm is positive on (1,infinity)) (current)
- 15:21, 21 October 2017 (diff | hist) . . (+360) . . N Mozyrska-Torres logarithm is positive on (1,infinity) (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. If $t \in (1,\infty) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) > 0$. ==Proof== ==References== {{PaperReference|The Natural Log...")
- 15:20, 21 October 2017 (diff | hist) . . (+353) . . N Mozyraska-Torres logarithm is negative on (0,1) (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$. ==Proof== ==References== {{PaperReference|The Natural Loga...")
- 15:18, 21 October 2017 (diff | hist) . . (+394) . . N Mozyrska-Torres logarithm is increasing (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. For all $t \in \mathbb{T}^{\kappa} \cap (0,\infty)$, $t \mapsto L_{\mathbb{T}}(t)$ is an increasing function. ==Proof==...")
- 15:16, 21 October 2017 (diff | hist) . . (+490) . . N Mozyrska-Torres logarithm on the reals (Created page with "==Theorem== The following formula holds: $$L_{\mathbb{R}}(t) = \ln(t),$$ where $L_{\mathbb{R}}$ denotes the Mozyrska-Torres logarithm on the Real numbers|time scale of r...")
- 15:13, 21 October 2017 (diff | hist) . . (+38) . . Mozyrska-Torres logarithm
- 15:11, 21 October 2017 (diff | hist) . . (+174) . . Delta derivative of Mozyrska-Torres logarithm
- 15:11, 21 October 2017 (diff | hist) . . (+31) . . Mozyrska-Torres logarithm
- 14:57, 21 October 2017 (diff | hist) . . (+24) . . Paper:Dorota Mozyrska/Functional series on time scales (current)
- 14:56, 21 October 2017 (diff | hist) . . (+45) . . Paper:Dorota Mozyrska/Functional series on time scales
- 14:56, 21 October 2017 (diff | hist) . . (+291) . . Paper:Dorota Mozyrska/Functional series on time scales
- 14:54, 21 October 2017 (diff | hist) . . (+16) . . Delta derivative
- 14:53, 21 October 2017 (diff | hist) . . (+131) . . Pre-differentiable
- 14:53, 21 October 2017 (diff | hist) . . (+139) . . Rd-continuous (current)
- 14:50, 21 October 2017 (diff | hist) . . (+141) . . Regulated (current)
- 14:49, 21 October 2017 (diff | hist) . . (+131) . . Delta derivative
- 14:48, 21 October 2017 (diff | hist) . . (+140) . . Left dense
- 14:48, 21 October 2017 (diff | hist) . . (+150) . . Right dense
- 14:47, 21 October 2017 (diff | hist) . . (+152) . . Left scattered
- 14:47, 21 October 2017 (diff | hist) . . (+158) . . Right scattered
- 14:46, 21 October 2017 (diff | hist) . . (+154) . . Forward graininess
- 14:46, 21 October 2017 (diff | hist) . . (-1) . . Backward jump
- 14:46, 21 October 2017 (diff | hist) . . (+157) . . Backward jump
- 14:45, 21 October 2017 (diff | hist) . . (+135) . . Forward jump
- 14:44, 21 October 2017 (diff | hist) . . (+295) . . Time scale
- 14:40, 21 October 2017 (diff | hist) . . (+290) . . N Paper:Dorota Mozyrska/Functional series on time scales (Created page with "{{Book|Functional series on time scales|2008|International Journal of Mathematics and Statistics||Dorota Mozyrska|author2=Ewa Pawluszewicz}} ===Online copies=== [http://www.s...")
- 00:53, 26 September 2017 (diff | hist) . . (-304) . . Main Page
- 12:59, 19 August 2017 (diff | hist) . . (+56) . . Inequality for Hilger real part (current)
- 12:58, 17 August 2017 (diff | hist) . . (+56) . . Inequality for Hilger real part
- 12:57, 17 August 2017 (diff | hist) . . (+186) . . N Inequality for Hilger real part (Created page with "==Theorem== The following inequality holds for $z \in \mathbb{C}_h$: $$-\dfrac{1}{h} < \mathrm{Re}_h(z) < \infty.$$ ==Proof== ==References== Category:Theorem Category...")
- 12:57, 17 August 2017 (diff | hist) . . (-242) . . Hilger real part
- 12:57, 17 August 2017 (diff | hist) . . (-153) . . Limit of Hilger real and imag parts yields classical (current)
- 16:16, 10 July 2017 (diff | hist) . . (+286) . . N Paper:Martin Bohner/A survey of exponential functions on time scales (Created page with "{{Book|A survey of exponential functions on time scales|2001|Revista Cubo Matematica Educacional||Martin Bohner|author2=Allan Peterson}} ===Online copies=== [http://www.math....") (current)
- 17:36, 7 July 2017 (diff | hist) . . (-30) . . Paper:Lynn Erbe/Square Integrability of Gaussian Bells on Time Scales (→Online copies) (current)
- 17:36, 7 July 2017 (diff | hist) . . (+14) . . Paper:Lynn Erbe/Square Integrability of Gaussian Bells on Time Scales
- 17:35, 7 July 2017 (diff | hist) . . (+37) . . Paper:John M. Davis/Bilateral Laplace Transforms on Time Scales: Convergence, Convolution, and the Characterization of Stationary Stochastic Time Series (current)
- 17:34, 7 July 2017 (diff | hist) . . (-18) . . Bilateral Laplace transform
- 17:34, 7 July 2017 (diff | hist) . . (+180) . . Bilateral Laplace transform
- 17:32, 7 July 2017 (diff | hist) . . (+440) . . N Paper:John M. Davis/Bilateral Laplace Transforms on Time Scales: Convergence, Convolution, and the Characterization of Stationary Stochastic Time Series (Created page with "{{Book|Bilateral Laplace Transforms on Time Scales: Convergence, Convolution, and the Characterization of Stationary Stochastic Time Series|2009|Circuits, Systems and Signal P...")
- 17:22, 7 July 2017 (diff | hist) . . (+52) . . Paper:Lynn Erbe/Square Integrability of Gaussian Bells on Time Scales
- 17:20, 7 July 2017 (diff | hist) . . (-33) . . Gaussian bell
- 17:19, 7 July 2017 (diff | hist) . . (+42) . . Gaussian bell
- 17:18, 7 July 2017 (diff | hist) . . (-37) . . Gaussian bell
- 17:17, 7 July 2017 (diff | hist) . . (+308) . . N Paper:Lynn Erbe/Square Integrability of Gaussian Bells on Time Scales (Created page with "{{Book|Square Integrability of Gaussian Bells on Time Scales|2005|Computers & Mathematics with Applications||Lynn Erbe|author2=Allan Peterson|author3=Moritz Simon}} ===Online...")
- 17:14, 7 July 2017 (diff | hist) . . (-73) . . Delta exponential
- 00:57, 30 May 2017 (diff | hist) . . (+15) . . Inverse cylinder transformation (→References) (current)
- 00:56, 30 May 2017 (diff | hist) . . (+537) . . N Inverse cylinder transformation (Created page with "Let $\mathbb{T}$ be a time scale. We define the inverse cylinder transformation $\xi_h \colon \mathbb{Z}_h \rightarrow \mathbb{C}_h$, where $\mathbb{Z}_h$ denotes the cy...")
- 00:52, 30 May 2017 (diff | hist) . . (+179) . . Cylinder transformation (current)
- 00:50, 30 May 2017 (diff | hist) . . (+461) . . N Cylinder strip (Created page with "The cylinder strip $\mathbb{Z}_h$ is defined for $h>1$ by $$\mathbb{Z}_h = \left\{ z \in \mathbb{C} \colon -\dfrac{\pi}{h} < \mathrm{Im}(z) \leq \dfrac{\pi}{h} \right\},$$ and...") (current)
- 00:49, 30 May 2017 (diff | hist) . . (+8) . . Hilger circle (→References)
- 00:42, 30 May 2017 (diff | hist) . . (+240) . . Hilger circle
- 00:41, 30 May 2017 (diff | hist) . . (-25) . . Hilger real axis
- 00:40, 30 May 2017 (diff | hist) . . (+49) . . Hilger complex plane
- 00:40, 30 May 2017 (diff | hist) . . (-16) . . Hilger alternating axis
- 00:38, 30 May 2017 (diff | hist) . . (+240) . . Hilger alternating axis
- 00:37, 30 May 2017 (diff | hist) . . (+254) . . Hilger real axis
- 00:36, 30 May 2017 (diff | hist) . . (+244) . . Hilger complex plane
- 00:34, 30 May 2017 (diff | hist) . . (+14) . . Causal time scale (current)
- 00:34, 30 May 2017 (diff | hist) . . (+331) . . N Causal time scale (Created page with "Let $\mathbb{T}$ be a time scale. We say that $\mathbb{T}$ is causal provided it contains no elements less than $0$. =Properties= =References= *{{PaperReference|A genera...")
- 00:32, 30 May 2017 (diff | hist) . . (-1) . . Paper:Robert J. Marks II/A generalized Fourier transform and convolution on time scales
- 00:29, 30 May 2017 (diff | hist) . . (+323) . . N Paper:Robert J. Marks II/A generalized Fourier transform and convolution on time scales (Created page with "{{Book|A generalized Fourier transform and convolution on time scales|2008|Journal of Mathematical Analysis and Applications||Robert J. Marks II|author2=Ian A. Gravagne|author...")
- 23:37, 29 May 2017 (diff | hist) . . (+270) . . N Paper:Gusein Sh. Guseinov/Integration on time scales (Created page with "{{Book|Integration on time scales|2003|Journal of Mathematical Analysis and Applications||Gusein Sh. Guseinov|}} ===Online copies=== [http://www.sciencedirect.com/science/art...") (current)
- 13:02, 10 March 2017 (diff | hist) . . (-980) . . Unilateral Laplace transform (→References)
- 13:01, 10 March 2017 (diff | hist) . . (+10) . . Unilateral Laplace transform
- 23:44, 14 February 2017 (diff | hist) . . (+272) . . N Delta Clairaut dynamic equation (Created page with "Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{R} \rightarrow \mathbb{R}$ be continuously differentiable. The delta Clairaut dynamic equation is $$y(t)=ty^...") (current)
- 17:47, 11 February 2017 (diff | hist) . . (+144) . . Jackson logarithm of a product (current)
- 17:46, 11 February 2017 (diff | hist) . . (-8) . . Delta exponential of Jackson logarithm (current)
- 17:46, 11 February 2017 (diff | hist) . . (+176) . . Delta exponential of Jackson logarithm
- 17:45, 11 February 2017 (diff | hist) . . (+32) . . Jackson logarithm of delta exponential (→References) (current)
- 17:43, 11 February 2017 (diff | hist) . . (+2) . . Jackson logarithm (current)
- 17:43, 11 February 2017 (diff | hist) . . (+20) . . Jackson logarithm (→References)
- 17:43, 11 February 2017 (diff | hist) . . (+11) . . Jackson logarithm of delta exponential
- 17:42, 11 February 2017 (diff | hist) . . (+97) . . Jackson logarithm of delta exponential
- 17:39, 11 February 2017 (diff | hist) . . (+341) . . N Jackson logarithm of a product (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. The following formula holds: $$\log_{\mathbb{T}}(f(t)g(t))=\log_{\mathbb{T}} f(t) \oplus \log_{\mathbb{T}} g(t),$$ where $\lo...")
- 17:37, 11 February 2017 (diff | hist) . . (+41) . . Jackson logarithm (→Properties)
- 17:36, 11 February 2017 (diff | hist) . . (+313) . . N Delta exponential of Jackson logarithm (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. The following formula holds: $$e_{\log_{\mathbb{T}} f}(t,s)=\dfrac{f(t)}{f(s)},$$ where $e_{\cdot}$ denotes the delta expon...")
- 17:34, 11 February 2017 (diff | hist) . . (-903) . . Jackson logarithm
- 17:33, 11 February 2017 (diff | hist) . . (+255) . . N Jackson logarithm of delta exponential (Created page with "==Theorem== The following formula holds: $$\log_{\mathbb{T}} e_p(t,s) = p(t),$$ where $\log_{\mathbb{T}}$ denotes the Jackson logarithm and $e_p$ denotes the delta expon...")
- 17:33, 11 February 2017 (diff | hist) . . (-238) . . Jackson logarithm
- 17:30, 11 February 2017 (diff | hist) . . (+16) . . Jackson logarithm
- 17:30, 11 February 2017 (diff | hist) . . (+87) . . Paper:Billy Jackson/The time scale logarithm (current)
- 17:27, 11 February 2017 (diff | hist) . . (-76) . . Paper:Billy Jackson/The time scale logarithm
- 17:26, 11 February 2017 (diff | hist) . . (-152) . . Jackson logarithm
- 17:24, 11 February 2017 (diff | hist) . . (-60) . . Jackson logarithm
- 17:22, 11 February 2017 (diff | hist) . . (+314) . . N Paper:Billy Jackson/The time scale logarithm (Created page with "{{Book|The time scale logarithm|2008|Applied Mathematics Letters||Billy Jackson|}} ===Online copies=== [http://ac.els-cdn.com/S0893965907001309/1-s2.0-S0893965907001309-main....")
- 17:09, 11 February 2017 (diff | hist) . . (+100) . . Mozyrska-Torres logarithm
- 17:03, 11 February 2017 (diff | hist) . . (+64) . . Euler-Cauchy logarithm
- 17:02, 11 February 2017 (diff | hist) . . (+1) . . Bohner logarithm (current)
- 17:02, 11 February 2017 (diff | hist) . . (+1) . . Euler-Cauchy logarithm
- 17:02, 11 February 2017 (diff | hist) . . (+2) . . Delta exponential dynamic equation (current)
- 17:02, 11 February 2017 (diff | hist) . . (-2) . . Delta exponential dynamic equation
- 17:01, 11 February 2017 (diff | hist) . . (+112) . . Paper:Martin Bohner/The logarithm on time scales (current)
- 17:00, 11 February 2017 (diff | hist) . . (+2) . . Bohner logarithm
- 17:00, 11 February 2017 (diff | hist) . . (+4) . . Bohner logarithm
- 17:00, 11 February 2017 (diff | hist) . . (-34) . . Delta exponential dynamic equation
- 16:59, 11 February 2017 (diff | hist) . . (+136) . . Delta exponential dynamic equation
- 16:59, 11 February 2017 (diff | hist) . . (+2) . . Euler-Cauchy logarithm
- 16:59, 11 February 2017 (diff | hist) . . (+38) . . Euler-Cauchy logarithm
- 16:58, 11 February 2017 (diff | hist) . . (-349) . . Euler-Cauchy logarithm
- 16:53, 11 February 2017 (diff | hist) . . (-50) . . Delta exponential dynamic equation (→See also)
- 16:53, 11 February 2017 (diff | hist) . . (+162) . . Delta exponential dynamic equation
- 23:27, 10 February 2017 (diff | hist) . . (+7) . . Bohner logarithm
- 23:05, 10 February 2017 (diff | hist) . . (+127) . . Euler-Cauchy dynamic equation (current)
- 23:03, 10 February 2017 (diff | hist) . . (+109) . . Bohner logarithm
- 23:00, 10 February 2017 (diff | hist) . . (+1) . . Euler-Cauchy dynamic equation
- 23:00, 10 February 2017 (diff | hist) . . (+307) . . N Euler-Cauchy dynamic equation (Created page with "Let $\mathbb{T} be a time scale and let $a, b \in \mathbb{R}$. The following dynamic equation is called the Euler-Cauchy dynamic equation: $$t \sigma(t) y^{\Delta \Del...")
- 22:59, 10 February 2017 (diff | hist) . . (0) . . m Euler-Cauchy logarithm (Tom moved page Cauchy-Euler logarithm to Euler-Cauchy logarithm over redirect)
- 22:59, 10 February 2017 (diff | hist) . . (+36) . . N Cauchy-Euler logarithm (Tom moved page Cauchy-Euler logarithm to Euler-Cauchy logarithm over redirect) (current)
- 22:53, 10 February 2017 (diff | hist) . . (+389) . . N Bohner logarithm sub a product (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $p, q \colon \mathbb{T} \rightarrow \mathbb{C}$. The following formula holds: $$L_{pq}(t,s)=L_p(t,s)+L_q(t,s)+\display...") (current)
- 22:49, 10 February 2017 (diff | hist) . . (-327) . . Bohner logarithm
- 22:45, 10 February 2017 (diff | hist) . . (-95) . . Paper:Martin Bohner/The logarithm on time scales
- 22:45, 10 February 2017 (diff | hist) . . (-1) . . MediaWiki:Sidebar
- 22:44, 10 February 2017 (diff | hist) . . (-1) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey (current)
- 22:44, 10 February 2017 (diff | hist) . . (-1) . . Paper:Dorota Mozyrska/The Natural Logarithm on Time Scales
- 22:44, 10 February 2017 (diff | hist) . . (+229) . . N Paper:Martin Bohner/The logarithm on time scales (Created page with "===Online copies=== [http://web.mst.edu/~bohner/papers/tlots.pdf hosted by Martin Bohner]<br /> ===References=== {{PaperReference|The logarithm on time scales|2005|Martin Boh...")
- 22:39, 10 February 2017 (diff | hist) . . (+2) . . Forward regressive
- 22:38, 10 February 2017 (diff | hist) . . (+18) . . Forward regressive
- 22:38, 10 February 2017 (diff | hist) . . (+104) . . Forward regressive
- 16:42, 9 February 2017 (diff | hist) . . (-181) . . Delta exponential dynamic equation
- 16:42, 9 February 2017 (diff | hist) . . (+50) . . Delta exponential dynamic equation
- 16:41, 9 February 2017 (diff | hist) . . (-16) . . Delta exponential dynamic equation
- 16:39, 9 February 2017 (diff | hist) . . (+25) . . Forward regressive
- 16:38, 9 February 2017 (diff | hist) . . (+26) . . Forward regressive
- 16:38, 9 February 2017 (diff | hist) . . (-1,845) . . Forward regressive (Replaced content with "Let $\mathbb{T}$ be a time scale. Let $p \colon \mathbb{T} \rightarrow \mathbb{C}$. We say that $p$ is forward regressive if for all $t \in \mathbb{T}^{\k...")
- 16:37, 9 February 2017 (diff | hist) . . (+36) . . Delta exponential dynamic equation
- 16:32, 9 February 2017 (diff | hist) . . (-40) . . Dynamic equation (→See Also) (current)
- 16:31, 9 February 2017 (diff | hist) . . (+40) . . Dynamic equation
- 16:29, 9 February 2017 (diff | hist) . . (+2) . . Delta exponential dynamic equation
- 16:26, 9 February 2017 (diff | hist) . . (+35) . . Dynamic equation
- 16:26, 9 February 2017 (diff | hist) . . (-1,269) . . Dynamic equation
- 16:22, 9 February 2017 (diff | hist) . . (+46) . . Dynamic equation (→See Also)
- 16:18, 9 February 2017 (diff | hist) . . (+42) . . Delta exponential dynamic equation
- 23:22, 8 February 2017 (diff | hist) . . (+2) . . Delta exponential
- 23:21, 8 February 2017 (diff | hist) . . (-2) . . Semigroup property of delta exponential (current)
- 23:21, 8 February 2017 (diff | hist) . . (0) . . m Delta exponential dynamic equation (Tom moved page Forward exponential dynamic equation to Delta exponential dynamic equation)
- 23:20, 8 February 2017 (diff | hist) . . (+8) . . Semigroup property of delta exponential
- 23:20, 8 February 2017 (diff | hist) . . (0) . . m Delta exponential dynamic equation (Tom moved page Exponential dynamic equation to Forward exponential dynamic equation)
- 23:20, 8 February 2017 (diff | hist) . . (-62) . . Delta exponential dynamic equation
- 23:19, 8 February 2017 (diff | hist) . . (+2) . . Semigroup property of delta exponential
- 23:18, 8 February 2017 (diff | hist) . . (+57) . . Delta exponential dynamic equation
- 23:18, 8 February 2017 (diff | hist) . . (+446) . . N Delta exponential dynamic equation (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following dynamic equation holds: $$y^{\Delta}(t)=p(t)y(t), \quad...")
- 23:15, 8 February 2017 (diff | hist) . . (+164) . . Semigroup property of delta exponential
- 23:13, 8 February 2017 (diff | hist) . . (+183) . . Delta exponential
- 23:13, 8 February 2017 (diff | hist) . . (+29) . . Semigroup property of delta exponential
- 23:12, 8 February 2017 (diff | hist) . . (+8) . . Semigroup property of delta exponential
- 03:33, 7 January 2017 (diff | hist) . . (+1) . . Main Page
- 00:07, 5 January 2017 (diff | hist) . . (+35) . . Delta derivative
- 00:07, 5 January 2017 (diff | hist) . . (+45) . . Delta mean value theorem (current)
- 23:59, 4 January 2017 (diff | hist) . . (+72) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 23:55, 4 January 2017 (diff | hist) . . (+154) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 23:53, 4 January 2017 (diff | hist) . . (+534) . . N Delta mean value theorem (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ be pre-differentiable with $D$. Then $|f^{\Delta}(t)| \leq g^{\Delt...")
- 23:51, 4 January 2017 (diff | hist) . . (+18) . . Regulated on compact interval is bounded (current)
- 23:42, 4 January 2017 (diff | hist) . . (+256) . . N Regulated on compact interval is bounded (Created page with "==Theorem== Every regulated function on a compact interval is bounded. ==Proof== ==References== * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bo...")
- 23:41, 4 January 2017 (diff | hist) . . (+34) . . Pre-differentiable
- 23:41, 4 January 2017 (diff | hist) . . (+152) . . Pre-differentiable
- 23:40, 4 January 2017 (diff | hist) . . (+43) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 23:39, 4 January 2017 (diff | hist) . . (+173) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 23:37, 4 January 2017 (diff | hist) . . (+40) . . Rd-continuous
- 23:37, 4 January 2017 (diff | hist) . . (+40) . . Forward jump
- 23:37, 4 January 2017 (diff | hist) . . (+56) . . Regulated
- 23:36, 4 January 2017 (diff | hist) . . (+4) . . Regulated
- 23:35, 4 January 2017 (diff | hist) . . (+31) . . Left dense
- 23:35, 4 January 2017 (diff | hist) . . (+32) . . Right dense
- 23:35, 4 January 2017 (diff | hist) . . (+182) . . N Left scattered (Created page with "Let $\mathbb{T}$ be a time scale. We say that $t \in \mathbb{T}$ is left scattered provided that $\nu(t)<t$, where $\nu$ denotes the backward jump. =See also= Left ...")
- 23:34, 4 January 2017 (diff | hist) . . (+189) . . N Right scattered (Created page with "Let $\mathbb{T}$ be a time scale. We say that $t \in \mathbb{T}$ is right scattered provided that $\sigma(t)>t$, where $\sigma$ denotes the forward jump. =See also= [...")
- 23:33, 4 January 2017 (diff | hist) . . (-1) . . Left dense
- 23:33, 4 January 2017 (diff | hist) . . (+152) . . N Left dense (Created page with "Let $\mathbb{T}$ be a time scale. We say that $t \in \mathbb{T}$ is left dense provided that $\nu(t)=t$, where $\nu$ denotes the backwards jump.")
- 23:32, 4 January 2017 (diff | hist) . . (+157) . . N Right dense (Created page with "Let $\mathbb{T}$ be a time scale. We say that $t \in \mathbb{T}$ is right dense provided that $\sigma(t)=t$, where $\sigma$ denotes the forward jump.")
- 23:32, 4 January 2017 (diff | hist) . . (-8) . . Regulated
- 23:31, 4 January 2017 (diff | hist) . . (+6) . . Forward jump is rd-continuous (current)
- 23:30, 4 January 2017 (diff | hist) . . (+293) . . N Forward jump is rd-continuous (Created page with "==Theorem== The forward jump function is rd-continuous. ==Proof== ==References== * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan ...")
- 23:29, 4 January 2017 (diff | hist) . . (+25) . . Continuous implies rd-continuous (current)
- 23:28, 4 January 2017 (diff | hist) . . (-9) . . Rd-continuous
- 23:28, 4 January 2017 (diff | hist) . . (0) . . m Regulated (Tom moved page Regulated function to Regulated)
- 23:28, 4 January 2017 (diff | hist) . . (+23) . . N Regulated function (Tom moved page Regulated function to Regulated) (current)
- 23:28, 4 January 2017 (diff | hist) . . (0) . . m Continuous (Tom moved page Continuity to Continuous) (current)
- 23:28, 4 January 2017 (diff | hist) . . (+24) . . N Continuity (Tom moved page Continuity to Continuous) (current)
- 23:28, 4 January 2017 (diff | hist) . . (+44) . . Rd-continuous implies regulated (current)
- 23:27, 4 January 2017 (diff | hist) . . (+370) . . N Rd-continuous implies regulated (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. If $f$ is continuous, then $f$ is regulated. ==Proof== ==Refer...")
- 23:26, 4 January 2017 (diff | hist) . . (+42) . . Rd-continuous
- 23:25, 4 January 2017 (diff | hist) . . (+26) . . Rd-continuous
- 23:25, 4 January 2017 (diff | hist) . . (+375) . . N Continuous implies rd-continuous (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. If $f$ is continuous, then $f$ is rd-continuous. ==Proof== ==R...")
- 23:24, 4 January 2017 (diff | hist) . . (+57) . . Rd-continuous
- 23:23, 4 January 2017 (diff | hist) . . (+83) . . Book:Martin Bohner/Dynamic Equations on Time Scales (→Contents)
- 23:23, 4 January 2017 (diff | hist) . . (+164) . . Rd-continuous
- 23:22, 4 January 2017 (diff | hist) . . (+159) . . Regulated
- 07:02, 30 December 2016 (diff | hist) . . (+261) . . N Paper:C.R. Adams/Linear q-difference equations (Created page with "{{Book|Linear q-difference equations|1931|Journal of Dynamical Systems & Geometric Theories||C.R. Adams|}} ===Online copies=== [https://projecteuclid.org/download/pdf_1/eucli...") (current)
- 11:17, 24 December 2016 (diff | hist) . . (+130) . . Timescalecalculus python library documentation (→On $\mathbb{T}=\{2,3,5,7,11,13,17\}$)
- 11:14, 24 December 2016 (diff | hist) . . (+377) . . Timescalecalculus python library documentation (→Delta exponential $e_p(t,s)$)
- 11:07, 24 December 2016 (diff | hist) . . (+12) . . Timescalecalculus python library documentation (→Delta exponential $e_p(t,s)$)
- 11:06, 24 December 2016 (diff | hist) . . (-40) . . Timescalecalculus python library documentation
- 11:05, 24 December 2016 (diff | hist) . . (+4) . . Timescalecalculus python library documentation (→Delta exponential $e_p(t,s)$)
- 11:05, 24 December 2016 (diff | hist) . . (+1,041) . . Timescalecalculus python library documentation
- 06:37, 23 December 2016 (diff | hist) . . (+389) . . Timescalecalculus python library documentation
- 06:34, 23 December 2016 (diff | hist) . . (+50) . . Backward graininess (current)
- 06:24, 23 December 2016 (diff | hist) . . (+287) . . N Delta derivative of constant (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{C}$ be a constant function. Then the following formula holds for all $t \in \...") (current)
- 06:23, 23 December 2016 (diff | hist) . . (+39) . . Delta derivative (→Properties of the $\Delta$-derivative)
- 06:22, 23 December 2016 (diff | hist) . . (+386) . . Timescalecalculus python library documentation (→Defining a time scale)
- 03:27, 19 December 2016 (diff | hist) . . (+16) . . Timescalecalculus python library documentation (→Defining a time scale)
- 03:21, 19 December 2016 (diff | hist) . . (+79) . . MediaWiki:Sidebar
- 03:12, 19 December 2016 (diff | hist) . . (-69) . . Timescalecalculus python library documentation
- 03:11, 19 December 2016 (diff | hist) . . (+207) . . Timescalecalculus python library documentation
- 03:09, 19 December 2016 (diff | hist) . . (-54) . . Timescalecalculus python library documentation
- 03:05, 19 December 2016 (diff | hist) . . (-29) . . Main Page
- 03:04, 19 December 2016 (diff | hist) . . (+204) . . Main Page
- 03:02, 19 December 2016 (diff | hist) . . (+950) . . N Timescalecalculus python library documentation (Created page with "{{lowercase}} This is the documentation for the Python repository [https://github.com/tomcuchta/timescalecalculus timescalecalculus]. =The basics= After extracting the files...")
- 03:02, 19 December 2016 (diff | hist) . . (0) . . Delta derivative of squaring function (current)
- 03:00, 19 December 2016 (diff | hist) . . (+346) . . N Delta derivative of squaring function (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. The following formula holds for $f \colon \mathbb{T} \rightarrow \mathbb{R}$ defined by $f(t)=t^2$: $$f^{\Delta}(t)=t \sigma(...")
- 02:59, 19 December 2016 (diff | hist) . . (+48) . . Delta derivative (→Properties of the $\Delta$-derivative)
- 02:50, 19 December 2016 (diff | hist) . . (+154) . . N Template:Lowercase (Created page with "<span style="display:none">{{DISPLAYTITLE:{{#if:{{NAMESPACE}}|{{NAMESPACE}}:|}}{{lcfirst:{{PAGENAME}}}}}}</span><noinclude> {{documentation}} </noinclude>") (current)
- 01:11, 19 December 2016 (diff | hist) . . (+10) . . Nabla exponential (current)
- 23:51, 11 December 2016 (diff | hist) . . (+37) . . Main Page
- 23:39, 11 December 2016 (diff | hist) . . (+71) . . Nabla sine (current)
- 23:38, 11 December 2016 (diff | hist) . . (+8) . . Nabla cosh (current)
- 23:38, 11 December 2016 (diff | hist) . . (0) . . m Dynamic equation for nabla cosh and nabla sinh (Tom moved page 2nd order dynamic equation for nabla cosh and nabla sinh to Dynamic equation for nabla cosh and nabla sinh) (current)
- 23:38, 11 December 2016 (diff | hist) . . (+60) . . N 2nd order dynamic equation for nabla cosh and nabla sinh (Tom moved page 2nd order dynamic equation for nabla cosh and nabla sinh to Dynamic equation for nabla cosh and nabla sinh) (current)
- 23:37, 11 December 2016 (diff | hist) . . (0) . . m Dynamic equation for nabla cosh and nabla sinh (Tom moved page Second order dynamic equation for nabla cosh to 2nd order dynamic equation for nabla cosh and nabla sinh)
- 23:37, 11 December 2016 (diff | hist) . . (+70) . . N Second order dynamic equation for nabla cosh (Tom moved page Second order dynamic equation for nabla cosh to 2nd order dynamic equation for nabla cosh and nabla sinh) (current)
- 23:37, 11 December 2016 (diff | hist) . . (+447) . . N Dynamic equation for nabla cosh and nabla sinh (Created page with "==Theorem== If $\gamma > 0$ with $\alpha^2\nu \in \mathcal{\nu}$, a regressive function, then the dynamic equation $$y^{\nabla \nabla}-\gamma^2 y=0$$ is solved by the func...")
- 23:35, 11 December 2016 (diff | hist) . . (-365) . . Nabla cosh
- 02:00, 11 December 2016 (diff | hist) . . (+83) . . Main Page
- 01:56, 11 December 2016 (diff | hist) . . (+77) . . Main Page
- 00:56, 11 December 2016 (diff | hist) . . (+2) . . Nth root of nonnegative integers (current)
- 02:15, 2 December 2016 (diff | hist) . . (-75) . . Delta exponential
- 02:15, 2 December 2016 (diff | hist) . . (+65) . . Cylinder transformation
- 02:14, 2 December 2016 (diff | hist) . . (+431) . . N Cylinder transformation (Created page with "Let $\mathbb{T}$ be a time scale. We define the cylinder transformation $\xi_h \colon \mathbb{C}_h \rightarrow \mathbb{Z}_h$, where $\mathbb{C}_h$ denotes the Hilger com...")
- 02:48, 17 November 2016 (diff | hist) . . (-1) . . Delta derivative of the delta integral (current)
- 22:13, 6 October 2016 (diff | hist) . . (-44) . . Delta integral over degenerate interval (current)
- 15:07, 25 September 2016 (diff | hist) . . (+30) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 15:06, 25 September 2016 (diff | hist) . . (+2) . . Delta derivative of classical polynomial (current)
- 15:05, 25 September 2016 (diff | hist) . . (+44) . . Delta derivative of classical polynomial
- 01:31, 24 September 2016 (diff | hist) . . (+11) . . Table:Delta hk (current)
- 00:23, 24 September 2016 (diff | hist) . . (+2) . . Delta differentiable implies continuous
- 00:22, 24 September 2016 (diff | hist) . . (+33) . . Delta hk
- 00:22, 24 September 2016 (diff | hist) . . (-63) . . Expected value of uniform distribution (current)
- 12:48, 23 September 2016 (diff | hist) . . (+2) . . Delta derivative of reciprocal of classical polynomial (current)
- 15:58, 22 September 2016 (diff | hist) . . (+15) . . Variance (current)
- 15:57, 22 September 2016 (diff | hist) . . (+15) . . Expected value (→Example) (current)
- 15:53, 22 September 2016 (diff | hist) . . (+10) . . Delta Lyapunov inequality
- 15:46, 22 September 2016 (diff | hist) . . (+24) . . Hilger real part
- 15:46, 22 September 2016 (diff | hist) . . (+5) . . Hilger pure imaginary
- 15:45, 22 September 2016 (diff | hist) . . (+10) . . Hilger imaginary part
- 15:43, 22 September 2016 (diff | hist) . . (+10) . . Forward circle minus
- 15:41, 22 September 2016 (diff | hist) . . (+9) . . Bilateral Laplace transform
- 15:40, 22 September 2016 (diff | hist) . . (0) . . Relationship between delta hk and delta gk (current)
- 21:00, 17 September 2016 (diff | hist) . . (+92) . . Mozyrska-Torres logarithm
- 20:56, 17 September 2016 (diff | hist) . . (+304) . . N Mozyrska-Torres logarithm at 1 (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale including $1$ and at least one other point $t$ such that $0< t < 1$. The following formula holds: $$L_{\mathbb{T}}(1)=0,$$ where $...")
- 20:56, 17 September 2016 (diff | hist) . . (+18) . . Mozyrska-Torres logarithm (→Properties)
- 20:55, 17 September 2016 (diff | hist) . . (+66) . . Delta derivative of Mozyrska-Torres logarithm
- 20:55, 17 September 2016 (diff | hist) . . (+71) . . Delta derivative of Mozyrska-Torres logarithm
- 20:54, 17 September 2016 (diff | hist) . . (+189) . . N Delta derivative of Mozyrska-Torres logarithm (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale including $1$ and at least one other point $t$ such that $0< t < 1$. The following formula holds: $$L_{\mathbb{T}}^{\Delta}(t) = \...")
- 20:54, 17 September 2016 (diff | hist) . . (+11) . . Mozyrska-Torres logarithm
- 20:53, 17 September 2016 (diff | hist) . . (+36) . . Paper:Dorota Mozyrska/The Natural Logarithm on Time Scales
- 20:52, 17 September 2016 (diff | hist) . . (+3) . . Mozyrska-Torres logarithm
- 20:50, 17 September 2016 (diff | hist) . . (+1) . . Paper:Dorota Mozyrska/The Natural Logarithm on Time Scales
- 20:50, 17 September 2016 (diff | hist) . . (+1) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 20:49, 17 September 2016 (diff | hist) . . (+26) . . MediaWiki:Sidebar
- 20:48, 17 September 2016 (diff | hist) . . (+20) . . Paper:Dorota Mozyrska/The Natural Logarithm on Time Scales
- 20:48, 17 September 2016 (diff | hist) . . (+243) . . N Paper:Dorota Mozyrska/The Natural Logarithm on Time Scales (Created page with "{{Book|The Natural Logarithm on Time Scales|2009|Journal of Dynamical Systems & Geometric Theories||Dorota Mozyrska|author2 = Delfim F. M. Torres}} ===Online copies=== [http:...")
- 00:46, 15 September 2016 (diff | hist) . . (+10) . . Nabla exponential
- 00:43, 15 September 2016 (diff | hist) . . (+15) . . Delta spq (current)
- 00:42, 15 September 2016 (diff | hist) . . (-137) . . Derivative of alternative delta sine (current)
- 00:41, 15 September 2016 (diff | hist) . . (-139) . . Derivative of alternative delta cosine (current)
- 00:41, 15 September 2016 (diff | hist) . . (-165) . . Pythagorean identity for alternate delta trigonometric functions (current)
- 00:41, 15 September 2016 (diff | hist) . . (+15) . . Delta cpq (→Properties) (current)
- 00:39, 15 September 2016 (diff | hist) . . (+10) . . Delta Wirtinger inequality (current)
- 00:39, 15 September 2016 (diff | hist) . . (-112) . . Delta Wirtinger inequality
- 00:38, 15 September 2016 (diff | hist) . . (+10) . . Delta Tschebycheff inequality (current)
- 00:38, 15 September 2016 (diff | hist) . . (+83) . . Delta Tschebycheff inequality
- 00:38, 15 September 2016 (diff | hist) . . (+44) . . Delta Opial inequality (current)
- 00:38, 15 September 2016 (diff | hist) . . (+44) . . Delta Minkowski inequality (current)
- 00:37, 15 September 2016 (diff | hist) . . (+10) . . Delta Markov inequality (current)
- 00:37, 15 September 2016 (diff | hist) . . (+87) . . Delta Markov inequality
- 00:37, 15 September 2016 (diff | hist) . . (-112) . . Delta Lyapunov inequality
- 00:36, 15 September 2016 (diff | hist) . . (+44) . . Delta Jensen inequality (current)
- 00:36, 15 September 2016 (diff | hist) . . (+44) . . Delta Gronwall inequality (current)
- 00:36, 15 September 2016 (diff | hist) . . (+44) . . Delta Cauchy-Schwarz inequality (current)
- 00:36, 15 September 2016 (diff | hist) . . (+44) . . Delta Bihari inequality (current)
- 00:36, 15 September 2016 (diff | hist) . . (+44) . . Delta Bernoulli inequality
- 00:36, 15 September 2016 (diff | hist) . . (+44) . . Delta Hölder inequality (current)
- 00:35, 15 September 2016 (diff | hist) . . (+12) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 00:35, 15 September 2016 (diff | hist) . . (+36) . . Delta Opial inequality
- 00:35, 15 September 2016 (diff | hist) . . (+13) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey (→Contents)
- 00:34, 15 September 2016 (diff | hist) . . (+36) . . Delta Bihari inequality
- 00:34, 15 September 2016 (diff | hist) . . (+13) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 00:34, 15 September 2016 (diff | hist) . . (+36) . . Delta Gronwall inequality
- 00:33, 15 September 2016 (diff | hist) . . (+46) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 00:32, 15 September 2016 (diff | hist) . . (+36) . . Delta Bernoulli inequality
- 00:31, 15 September 2016 (diff | hist) . . (+13) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 00:31, 15 September 2016 (diff | hist) . . (+36) . . Delta Jensen inequality
- 00:30, 15 September 2016 (diff | hist) . . (+13) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 00:30, 15 September 2016 (diff | hist) . . (+10) . . Delta Minkowski inequality
- 00:30, 15 September 2016 (diff | hist) . . (-120) . . Delta Minkowski inequality
- 00:30, 15 September 2016 (diff | hist) . . (+10) . . Delta Cauchy-Schwarz inequality
- 00:29, 15 September 2016 (diff | hist) . . (+13) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 00:28, 15 September 2016 (diff | hist) . . (-120) . . Delta Cauchy-Schwarz inequality
- 00:28, 15 September 2016 (diff | hist) . . (0) . . Delta Hölder inequality
- 00:27, 15 September 2016 (diff | hist) . . (0) . . Delta Hölder inequality
- 00:19, 15 September 2016 (diff | hist) . . (+13) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 00:16, 15 September 2016 (diff | hist) . . (-173) . . Delta Hölder inequality
- 00:07, 15 September 2016 (diff | hist) . . (+7,617) . . N Template:PaperReference (Created page with "<!-- This excerpt is here for ease of understanding the wiki code for author refs. Might be expanded to aid readability of the book reference as well. {{AuthorRef|{{{3}}}}} {...") (current)
- 00:07, 15 September 2016 (diff | hist) . . (+63) . . Delta Hölder inequality
- 00:04, 15 September 2016 (diff | hist) . . (+467) . . Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey
- 00:03, 15 September 2016 (diff | hist) . . (-146) . . Delta Opial inequality
- 00:02, 15 September 2016 (diff | hist) . . (-140) . . Delta Bihari inequality
- 00:01, 15 September 2016 (diff | hist) . . (-146) . . Delta Gronwall inequality
- 23:59, 14 September 2016 (diff | hist) . . (-157) . . Delta Jensen inequality
- 23:47, 14 September 2016 (diff | hist) . . (+289) . . N Paper:Ravi Agarwal/Inequalities on Time Scales: A Survey (Created page with "{{Book|Inequalities on Time Scales: A Survey|2001|Mathematical Inequalities & Applications||Ravi Agarwal|author2 = Martin Bohner| author3 = Allan Peterson}} ===Online copies=...")
- 23:46, 14 September 2016 (diff | hist) . . (+192) . . N Template:Date (Created page with "{{#if: {{{day|}}} |${{{day}}}$ {{{month}}} ${{{year}}}$|{{#if: {{{month|}}} |{{{month}}} ${{{year}}}$|{{#if: {{{circa|}}} |c. ${{{circa}}}$|${{{1}}}$}}}}}}{{#if: {{{era|}}} |&...") (current)
- 23:36, 14 September 2016 (diff | hist) . . (0) . . Delta Bernoulli inequality
- 23:36, 14 September 2016 (diff | hist) . . (+10) . . Delta Bernoulli inequality
- 23:35, 14 September 2016 (diff | hist) . . (-156) . . Delta Bernoulli inequality
- 01:07, 23 August 2016 (diff | hist) . . (+130) . . Main Page (→Special functions on time scales)
- 01:06, 23 August 2016 (diff | hist) . . (+25) . . Main Page (→$\Diamond_{\alpha}$-calculus)
- 01:06, 23 August 2016 (diff | hist) . . (+10) . . Main Page (→$\nabla$-calculus)
- 01:06, 23 August 2016 (diff | hist) . . (+105) . . Main Page (→$\Delta$-calculus)
- 01:05, 23 August 2016 (diff | hist) . . (+215) . . Main Page (→Calculus on time scales)
- 01:01, 23 August 2016 (diff | hist) . . (+64) . . Nabla derivative (current)
- 00:58, 23 August 2016 (diff | hist) . . (+153) . . Nabla derivative at left-scattered (current)
- 00:57, 23 August 2016 (diff | hist) . . (+215) . . N Nabla derivative at left-scattered (Created page with "==Theorem== If $f$ is continuous at $t$ and $t$ is left-scattered, then $$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)}.$$ ==Proof== ==References== ...")
- 00:55, 23 August 2016 (diff | hist) . . (-229) . . Nabla derivative
- 00:54, 23 August 2016 (diff | hist) . . (+190) . . N Nabla differentiable implies continuous (Created page with "==Theorem== If $f$ is nabla differentiable at $t$, then $f$ is continuous at $t$. ==Proof== ==References== Category:Theorem Cate...") (current)
- 00:53, 23 August 2016 (diff | hist) . . (-221) . . Nabla derivative (→Properties of the $\nabla$-derivative)
- 00:31, 23 August 2016 (diff | hist) . . (-159) . . Relationship between delta derivative and nabla derivative (current)
- 23:46, 22 August 2016 (diff | hist) . . (-1,318) . . Delta integral (current)
- 23:37, 22 August 2016 (diff | hist) . . (+41) . . Delta integral
- 23:35, 22 August 2016 (diff | hist) . . (+87) . . Delta derivative of the delta integral
- 23:34, 22 August 2016 (diff | hist) . . (+181) . . N Delta derivative of the delta integral (Created page with "==Theorem== The following formula holds: $$\left( \int_{t_0}^x f(\tau) \Delta \tau) \right)^{\Delta} = f(x).$$ ==Proof== ==References== Category:Theorem Category:Unpr...")
- 23:34, 22 August 2016 (diff | hist) . . (-268) . . Delta integral (→Properties of $\Delta$-integrals)
- 23:33, 22 August 2016 (diff | hist) . . (+255) . . N Delta integral of delta derivative (Created page with "==Theorem== The following formula holds: $$\int_a^b f^{\Delta}(t) \Delta t = f(b)-f(a),$$ where $\int$ denotes the delta integral and $f^{\Delta}$ denotes the delta deri...") (current)
- 23:33, 22 August 2016 (diff | hist) . . (-250) . . Delta integral (→Properties of $\Delta$-integrals)
- 23:32, 22 August 2016 (diff | hist) . . (+221) . . N Delta integral of nonnegative function (Created page with "==Theorem== If $f(t) \geq 0$ for all $a \leq t < b$ then $$\displaystyle\int_a^b f(t) \Delta t \geq 0,$$ where $\int$ denotes the delta integral. ==Proof== ==References...") (current)
- 23:31, 22 August 2016 (diff | hist) . . (-226) . . Delta integral (→Properties of $\Delta$-integrals)
- 23:28, 22 August 2016 (diff | hist) . . (+263) . . N Modulus of delta integral (Created page with "==Theorem== Let $|f(t)| \leq g(t)$ on $[a,b)$. The following formula holds: $$\left| \int_a^b f(t) \Delta t \right| \leq \int_a^b g(t) \Delta t,$$ where $\int$ denotes the ...") (current)
- 23:27, 22 August 2016 (diff | hist) . . (-255) . . Delta integral (→Properties of $\Delta$-integrals)
- 23:26, 22 August 2016 (diff | hist) . . (+187) . . N Delta integral over degenerate interval (Created page with "==Theorem== The following formula holds: $$\int_a^a f(t) \Delta t = 0,$$ where $\int$ denotes the delta integral. ==Proof== ==References== Category:Theorem Categor...")
- 23:26, 22 August 2016 (diff | hist) . . (-191) . . Delta integral (→Properties of $\Delta$-integrals)
- 23:26, 22 August 2016 (diff | hist) . . (+45) . . Integration by parts for delta integrals with no sigma in integrand
- 23:25, 22 August 2016 (diff | hist) . . (+220) . . N Integration by parts for delta integrals with no sigma in integrand (Created page with "==Theorem== The following formula holds: $$\int_a^b f(t) g^{\Delta}(t) \Delta t = (fg)(b) - (fg)(a) - \int_a^b f^{\Delta}(t) g(\sigma(t)) \Delta t.$$ ==Proof== ==References=...")
- 23:25, 22 August 2016 (diff | hist) . . (+12) . . Delta integral (→Properties of $\Delta$-integrals)
- 23:25, 22 August 2016 (diff | hist) . . (-273) . . Delta integral (→Properties of $\Delta$-integrals)
- 23:24, 22 August 2016 (diff | hist) . . (+263) . . N Integration by parts for delta integrals with sigma in integrand (Created page with "==Theorem== The following formula holds: $$\int_a^b f(\sigma(t))g^{\Delta}(t) \Delta t = (fg)(b) - (fg)(a) - \int_a^b f^{\Delta}(t)g(t) \Delta t,$$ where $\int$ denotes the ...")
- 23:24, 22 August 2016 (diff | hist) . . (-273) . . Delta integral (→Properties of $\Delta$-integrals)
- 23:23, 22 August 2016 (diff | hist) . . (+43) . . Delta integrals are additive over intervals (current)
- 23:22, 22 August 2016 (diff | hist) . . (+189) . . N Delta integrals are additive over intervals (Created page with "==Theorem== The following formula holds: $$\int_a^b f(t) \Delta t = \int_a^c f(t) \Delta t + \int_c^b f(t) \Delta t.$$ ==Proof== ==References== Category:Theorem Categ...")
- 23:22, 22 August 2016 (diff | hist) . . (-234) . . Delta integral (→Properties of $\Delta$-integrals)
- 22:52, 22 August 2016 (diff | hist) . . (+210) . . N Interchanging limits of delta integral (Created page with "==Theorem== The following formula holds: $$\int_a^b f(t) \Delta t = -\int_b^a f(t) \Delta t,$$ where $\int$ denotes the delta integral. ==Proof== ==References== Categ...") (current)
- 22:52, 22 August 2016 (diff | hist) . . (-512) . . Delta integral (→Properties of $\Delta$-integrals)
- 22:49, 22 August 2016 (diff | hist) . . (+312) . . N Delta integral is linear (Created page with "==Theorem== The delta integral is linear, i.e. for any $\alpha, \beta \in \mathbb{C}$, $$\displaystyle\int_s^t \alpha f(t) + \beta g(t) \Delta t = \alpha \displaystyle\in...") (current)
- 22:48, 22 August 2016 (diff | hist) . . (-131) . . Delta integral (→Properties of $\Delta$-integrals)
- 22:47, 22 August 2016 (diff | hist) . . (+108) . . Delta integral (→Properties of $\Delta$-integrals)
- 22:40, 22 August 2016 (diff | hist) . . (-228) . . Delta integral (→Properties of $\Delta$-integrals)
- 22:40, 22 August 2016 (diff | hist) . . (0) . . m Delta integral from t to sigma(t) (Tom moved page Integral from t to sigma(t) to Delta integral from t to sigma(t)) (current)
- 22:40, 22 August 2016 (diff | hist) . . (+47) . . N Integral from t to sigma(t) (Tom moved page Integral from t to sigma(t) to Delta integral from t to sigma(t)) (current)
- 22:39, 22 August 2016 (diff | hist) . . (+40) . . Delta integral from t to sigma(t)
- 22:39, 22 August 2016 (diff | hist) . . (+91) . . Delta integral from t to sigma(t)
- 22:38, 22 August 2016 (diff | hist) . . (+167) . . N Delta integral from t to sigma(t) (Created page with "==Theorem== The following formula holds: $$\int_t^{\sigma(t)} f(\tau) \Delta \tau = \mu(t)f(t)$$ ==Proof== ==References== Category:Theorem Category:Unproven")
- 22:37, 22 August 2016 (diff | hist) . . (-526) . . Delta integral
- 23:10, 14 July 2016 (diff | hist) . . (+14) . . Forward circle plus
- 23:10, 14 July 2016 (diff | hist) . . (+9) . . Regressive functions form an abelian group under circle plus (current)
- 23:09, 14 July 2016 (diff | hist) . . (0) . . Regressive functions form an abelian group under circle plus
- 23:09, 14 July 2016 (diff | hist) . . (+210) . . Regressive functions form an abelian group under circle plus
- 23:07, 14 July 2016 (diff | hist) . . (+143) . . N Regressive functions form an abelian group under circle plus (Created page with "==Theorem== The structure $(\mathbb{C}_h,\oplus_h)$ is an Abelian group. ==Proof== ==References== Category:Theorem Category:Unproven")
- 23:06, 14 July 2016 (diff | hist) . . (-169) . . Forward circle plus
- 21:42, 14 July 2016 (diff | hist) . . (-154) . . Hilger real part oplus Hilger imaginary part equals z (current)
- 21:34, 14 July 2016 (diff | hist) . . (+20) . . Forward circle plus
- 21:33, 14 July 2016 (diff | hist) . . (-136) . . Circle minus inverse of circle plus (current)
- 02:27, 11 June 2016 (diff | hist) . . (+1) . . Delta cosine
- 02:26, 11 June 2016 (diff | hist) . . (-3) . . Delta cosine
- 06:23, 10 June 2016 (diff | hist) . . (-376) . . Riccati equation (current)
- 06:13, 10 June 2016 (diff | hist) . . (+84) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 06:13, 10 June 2016 (diff | hist) . . (+755) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 06:09, 10 June 2016 (diff | hist) . . (-1) . . Delta derivative of sum (current)
- 06:08, 10 June 2016 (diff | hist) . . (+1) . . Delta simple useful formula (current)
- 06:06, 10 June 2016 (diff | hist) . . (+16) . . Forward jump
- 06:05, 10 June 2016 (diff | hist) . . (+145) . . Time scale
- 06:05, 10 June 2016 (diff | hist) . . (+25) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 06:03, 10 June 2016 (diff | hist) . . (+44) . . Delta derivative of reciprocal of classical polynomial
- 06:02, 10 June 2016 (diff | hist) . . (-159) . . Relationship between nabla derivative and delta derivative (current)
- 06:01, 10 June 2016 (diff | hist) . . (+116) . . Delta derivative
- 06:00, 10 June 2016 (diff | hist) . . (+537) . . N Delta derivative of reciprocal of classical polynomial (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale, let $\alpha$ a constant, let $m \in \mathbb{N}$, and define $g\colon \mathbb{T} \rightarrow \mathbb{R}$ by $g(t)=\dfrac{1}{(t...")
- 05:53, 10 June 2016 (diff | hist) . . (+54) . . Delta derivative of classical polynomial
- 05:53, 10 June 2016 (diff | hist) . . (+500) . . N Delta derivative of classical polynomial (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale, let $\alpha \in \mathbb{R}$, let $m \in \mathbb{N}$, and define $f \colon \mathbb{T} \rightarrow \mathbb{R}$ by $f(t)=(t-\alp...")
- 05:48, 10 June 2016 (diff | hist) . . (+20) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 05:47, 10 June 2016 (diff | hist) . . (+24) . . MediaWiki:Sidebar
- 05:47, 10 June 2016 (diff | hist) . . (+372) . . Delta derivative
- 05:45, 10 June 2016 (diff | hist) . . (+44) . . Delta derivative of sum
- 05:45, 10 June 2016 (diff | hist) . . (+44) . . Delta derivative of constant multiple (current)
- 05:45, 10 June 2016 (diff | hist) . . (+44) . . Delta derivative of product (1) (current)
- 05:44, 10 June 2016 (diff | hist) . . (+44) . . Delta derivative of product (2) (current)
- 05:44, 10 June 2016 (diff | hist) . . (+55) . . Delta derivative of quotient (current)
- 05:44, 10 June 2016 (diff | hist) . . (+62) . . Delta derivative of quotient
- 05:41, 10 June 2016 (diff | hist) . . (+579) . . N Delta derivative of reciprocal (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale, $t \in \mathbb{T}^{\kappa}$, $f \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable, and $f(t...")
- 05:41, 10 June 2016 (diff | hist) . . (+2) . . Delta derivative of product (2)
- 05:41, 10 June 2016 (diff | hist) . . (+551) . . N Delta derivative of quotient (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale, $t \in \mathbb{T}^{\kappa}$, $f \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable, and $f(t...")
- 05:37, 10 June 2016 (diff | hist) . . (0) . . Delta derivative of product (2)
- 05:37, 10 June 2016 (diff | hist) . . (+526) . . N Delta derivative of product (2) (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable. Then the product function $fg$ i...")
- 05:36, 10 June 2016 (diff | hist) . . (-1) . . Delta derivative of constant multiple
- 05:36, 10 June 2016 (diff | hist) . . (-40) . . Delta derivative of constant multiple
- 05:35, 10 June 2016 (diff | hist) . . (+1) . . Delta derivative of product (1)
- 05:35, 10 June 2016 (diff | hist) . . (+534) . . N Delta derivative of product (1) (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable. Then the product function $fg$ i...")
- 05:34, 10 June 2016 (diff | hist) . . (+521) . . N Delta derivative of constant multiple (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ delta differentiable. Then the product function $fg$ i...")
- 05:31, 10 June 2016 (diff | hist) . . (+517) . . N Delta derivative of sum (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale and let $f,g \colon \mathbb{T} \rightarrow \mathbb{R}$ be delta differentiable at $t$. Then the function ...")
- 05:28, 10 June 2016 (diff | hist) . . (+6) . . Delta derivative at right-dense
- 05:27, 10 June 2016 (diff | hist) . . (+6) . . Delta simple useful formula
- 05:26, 10 June 2016 (diff | hist) . . (+173) . . Delta simple useful formula
- 05:24, 10 June 2016 (diff | hist) . . (+6) . . Delta derivative at right-dense
- 05:24, 10 June 2016 (diff | hist) . . (+5) . . Delta derivative at right-scattered
- 05:24, 10 June 2016 (diff | hist) . . (+1) . . Delta differentiable implies continuous
- 05:24, 10 June 2016 (diff | hist) . . (+3) . . Delta differentiable implies continuous
- 05:23, 10 June 2016 (diff | hist) . . (+504) . . N Delta derivative at right-dense (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale, $t \in \mathbb{T}$ be right-dense. Then $f \colon \mathbb{T} \rightarrow \mathbb{R}$ is delta derivative|delta differen...")
- 05:19, 10 June 2016 (diff | hist) . . (0) . . Delta differentiable implies continuous
- 05:19, 10 June 2016 (diff | hist) . . (0) . . m Delta derivative at right-scattered (Tom moved page Delta derivative at right scattered to Delta derivative at right-scattered)
- 05:19, 10 June 2016 (diff | hist) . . (+49) . . N Delta derivative at right scattered (Tom moved page Delta derivative at right scattered to Delta derivative at right-scattered) (current)
- 05:19, 10 June 2016 (diff | hist) . . (+218) . . Delta derivative at right-scattered
- 05:18, 10 June 2016 (diff | hist) . . (+4) . . Delta derivative
- 05:17, 10 June 2016 (diff | hist) . . (0) . . m Delta differentiable implies continuous (Tom moved page Delta derivative implies continuous to Delta differentiable implies continuous)
- 05:17, 10 June 2016 (diff | hist) . . (+53) . . N Delta derivative implies continuous (Tom moved page Delta derivative implies continuous to Delta differentiable implies continuous) (current)
- 05:17, 10 June 2016 (diff | hist) . . (-161) . . Delta derivative
- 05:16, 10 June 2016 (diff | hist) . . (+359) . . N Delta derivative at right-scattered (Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be continuous and right-scattered at $t \in \mathbb{T}$. Then $$f^{\...")
- 05:13, 10 June 2016 (diff | hist) . . (+35) . . Delta differentiable implies continuous
- 05:12, 10 June 2016 (diff | hist) . . (-2,305) . . Delta derivative
- 05:10, 10 June 2016 (diff | hist) . . (+16) . . Induction on time scales (current)
- 05:09, 10 June 2016 (diff | hist) . . (+21) . . Induction on time scales
- 03:23, 10 June 2016 (diff | hist) . . (+169) . . Forward jump
- 03:23, 10 June 2016 (diff | hist) . . (+7,615) . . N Template:BookReference (Created page with "<!-- This excerpt is here for ease of understanding the wiki code for author refs. Might be expanded to aid readability of the book reference as well. {{AuthorRef|{{{3}}}}} {...") (current)
- 03:19, 10 June 2016 (diff | hist) . . (+1,956) . . Book:Martin Bohner/Dynamic Equations on Time Scales
- 03:11, 10 June 2016 (diff | hist) . . (+203) . . N Book:Martin Bohner/Dynamic Equations on Time Scales (Created page with "{{Book|Dynamic Equations on Time Scales||||Martin Bohner|author2=Allan Peterson}} ===Online versions=== [http://web.mst.edu/~bohner/sample.pdf Chapters 1-3 hosted by Martin B...")
- 03:11, 10 June 2016 (diff | hist) . . (+392) . . N Template:AuthorRef (Created page with "<noinclude> This template is to be used to provide a link to the authorship of an entry from (mainly) the Books page. It can be called by: * <code><nowiki>{{Au...") (current)
- 03:10, 10 June 2016 (diff | hist) . . (+3,208) . . N Template:Book (Created page with "<noinclude> This template is used to provide a standard header for a book or other publication. Can be called by: * <code><nowiki>{{Book|Name of book|Year of publication|Publ...") (current)
- 02:42, 10 June 2016 (diff | hist) . . (-125) . . Derivative of delta sinh (current)
- 02:00, 10 June 2016 (diff | hist) . . (+33) . . Delta sine
- 01:59, 10 June 2016 (diff | hist) . . (-24) . . Delta sine
- 01:59, 10 June 2016 (diff | hist) . . (-144) . . Relationship between delta hk and delta gk
- 01:58, 10 June 2016 (diff | hist) . . (-118) . . Zeros of delta gk (current)
- 22:22, 9 June 2016 (diff | hist) . . (-161) . . Relationship between nabla exponential and delta exponential (current)
- 22:22, 9 June 2016 (diff | hist) . . (-161) . . Relationship between delta exponential and nabla exponential (current)
- 22:21, 9 June 2016 (diff | hist) . . (-151) . . Quotient of delta exponentials with fixed t and s (current)
- 22:21, 9 June 2016 (diff | hist) . . (-150) . . Product of delta exponentials with fixed t and s (current)
- 22:20, 9 June 2016 (diff | hist) . . (-133) . . Reciprocal of delta exponential (current)
- 22:20, 9 June 2016 (diff | hist) . . (-123) . . Delta simple useful formula
- 22:19, 9 June 2016 (diff | hist) . . (-128) . . Delta exponential with t=s (current)
- 21:31, 9 June 2016 (diff | hist) . . (-128) . . Delta exponential with p=0 (current)
- 21:31, 9 June 2016 (diff | hist) . . (-141) . . Semigroup property of delta exponential
- 21:30, 9 June 2016 (diff | hist) . . (-161) . . Delta hyperbolic trigonometric second order dynamic equation (current)
- 21:30, 9 June 2016 (diff | hist) . . (-128) . . Delta cosh minus delta sinh (current)
- 21:29, 9 June 2016 (diff | hist) . . (-125) . . Derivative of delta cosh (current)
- 21:29, 9 June 2016 (diff | hist) . . (0) . . Delta cosine (→Properties)
- 21:29, 9 June 2016 (diff | hist) . . (0) . . Delta cosine (→Properties)
- 21:28, 9 June 2016 (diff | hist) . . (-126) . . Derivative of Delta sine (current)
- 21:28, 9 June 2016 (diff | hist) . . (-150) . . Sum of squares of delta cosine and delta sine (current)
- 21:27, 9 June 2016 (diff | hist) . . (+42) . . Derivative of delta cosine
- 21:26, 9 June 2016 (diff | hist) . . (-171) . . Derivative of delta cosine
- 21:25, 9 June 2016 (diff | hist) . . (+50) . . Delta sinh
- 21:24, 9 June 2016 (diff | hist) . . (+40) . . Delta sine
- 21:24, 9 June 2016 (diff | hist) . . (+30) . . Delta hk
- 21:24, 9 June 2016 (diff | hist) . . (+30) . . Delta gk
- 21:23, 9 June 2016 (diff | hist) . . (+5) . . Delta hk
- 21:23, 9 June 2016 (diff | hist) . . (+10) . . Delta gk
- 21:23, 9 June 2016 (diff | hist) . . (+10) . . Delta exponential
- 21:22, 9 June 2016 (diff | hist) . . (+80) . . Delta exponential
- 21:21, 9 June 2016 (diff | hist) . . (+45) . . Delta cosh
- 21:21, 9 June 2016 (diff | hist) . . (+16) . . Delta cosine
- 07:16, 8 June 2016 (diff | hist) . . (-25) . . MediaWiki:Sidebar
- 23:00, 2 June 2016 (diff | hist) . . (+170) . . Delta cpq
- 23:00, 2 June 2016 (diff | hist) . . (+551) . . N Derivative of alternative delta sine (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a [[time scale]...")
- 22:59, 2 June 2016 (diff | hist) . . (-9) . . Derivative of alternative delta cosine
- 22:58, 2 June 2016 (diff | hist) . . (+562) . . N Derivative of alternative delta cosine (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a ...")
- 22:57, 2 June 2016 (diff | hist) . . (+2) . . Pythagorean identity for alternate delta trigonometric functions
- 22:57, 2 June 2016 (diff | hist) . . (+534) . . N Pythagorean identity for alternate delta trigonometric functions (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\m...")
- 22:55, 2 June 2016 (diff | hist) . . (+170) . . Delta spq
- 22:53, 2 June 2016 (diff | hist) . . (+337) . . N Delta spq (Created page with "Let $\mathbb{T}$ be a time scale and let $p$ and $q$ be rd-continuous functions that satisfy the relation $2p(t)+\mu(t)(p(t)^2+q(t)^2)=0$. The (alternative) delta sine fun...")
- 22:52, 2 June 2016 (diff | hist) . . (+32) . . Delta cpq
- 22:52, 2 June 2016 (diff | hist) . . (+300) . . N Delta cpq (Created page with "Let $\mathbb{T}$ be a time scale and let $p$ and $q$ be rd-continuous functions that satisfy the relation $2p(t)+\mu(t)(p(t)^2+q(t)^2)=0$. The (alternative) cosine functio...")
- 22:49, 2 June 2016 (diff | hist) . . (+24) . . Main Page (→Special functions on time scales)
- 22:48, 2 June 2016 (diff | hist) . . (+112) . . Main Page (→Special functions on time scales)
- 22:39, 2 June 2016 (diff | hist) . . (-76) . . Main Page
- 22:38, 2 June 2016 (diff | hist) . . (-59) . . Main Page (→$\Delta$-calculus)
- 22:38, 2 June 2016 (diff | hist) . . (-31) . . Main Page (→Special functions on time scales)
- 22:37, 2 June 2016 (diff | hist) . . (0) . . Delta sinh
- 22:37, 2 June 2016 (diff | hist) . . (-31) . . Delta sinh
- 22:36, 2 June 2016 (diff | hist) . . (+17) . . Delta sinh
- 22:35, 2 June 2016 (diff | hist) . . (+16) . . Delta sine
- 22:34, 2 June 2016 (diff | hist) . . (+17) . . Delta exponential
- 22:33, 2 June 2016 (diff | hist) . . (+17) . . Delta cosh
- 22:32, 2 June 2016 (diff | hist) . . (-1) . . Delta cosine
- 22:32, 2 June 2016 (diff | hist) . . (-2) . . Delta cosine (→See Also)
- 22:32, 2 June 2016 (diff | hist) . . (-13) . . Delta cosine
- 22:32, 2 June 2016 (diff | hist) . . (+87) . . Delta cosine
- 22:31, 2 June 2016 (diff | hist) . . (+17) . . Delta gk
- 22:26, 2 June 2016 (diff | hist) . . (+127) . . Delta special functions footer
- 22:26, 2 June 2016 (diff | hist) . . (+1,055) . . N File:Integerdeltagk,k=2,s=0glyph.png (Category:deltagkglyph Category:glyph Category:timescale:integers Category:deltagk <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 2.4...) (current)
- 22:22, 2 June 2016 (diff | hist) . . (+1,055) . . N File:Integerdeltagk,k=3,s=0glyph.png (Category:deltagkglyph Category:glyph Category:timescale:integers Category:deltagk <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 2.4...) (current)
- 22:19, 2 June 2016 (diff | hist) . . (+1,061) . . N File:Integergk,k=4,s=0plot.png (Category:plot Category:deltagk Category:timescale:integers Category:specialfunction <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 1...) (current)
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